IGCSE · 4MA1 · Topic

Number Toolkit: past paper questions & worked solutions

Every Number Toolkit question from the 4MA1 papers in our bank, 2022–2026, plus original Elite practice questions, sorted from easiest to hardest. Try each one first, then open the worked solution.

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5questions

14marks in total

6%of papers (3 of 54) include it

1/4/0easy / medium / hard

Questions, easiest first

Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.

1. Elite Practice · Q37

Easy2 marks

Elite Practice Question 37 (2 marks): Number Toolkit – 37 Use the information that 23 x 47 = 1081 to write down the value of (a) 2.3 x 4.7 (b) 1081 ÷ 4.7. (Total for Question 37 is 2 marks)

Show worked solution

(a) Each number is ten times smaller
$2.3\times4.7=1081\div100=10.81$
(b) Reverse the multiplication
$1081\div47=23$, and $4.7$ is ten times smaller than $47$, so $1081\div4.7=230$.

Final answer

(a) $10.81$ (b) $230$

2. Jun 2026 P2H · Q1

Medium3 marks

Jun 2026 P2H Question 1 (3 marks): Number Toolkit – 1 Write 4500 as a product of powers of its prime factors. Show your working clearly. (Total for Question 1 is 3 marks)

Show worked solution

Solution | Step 1
\[4500=45\times100=(9\times5)(4\times25).\]
Split into factors that are easy to prime-factorise.
Solution | Step 2
\[4500=(3^2\times5)(2^2\times5^2)=2^2\times3^2\times5^3.\]
Express each factor as prime powers and combine powers of 5.

Final answer

$2^2\times3^2\times5^3$

3. Jun 2026 P1HR · Q2

Medium3 marks

Jun 2026 P1HR Question 2 (3 marks): Number Toolkit – 2 Write 504 as a product of powers of its prime factors. Show your working clearly. (Total for Question 2 is 3 marks)

Show worked solution

Solution | Step 1
\[504=2\times252=2^2\times126=2^3\times63.\]
Divide repeatedly by the prime 2.
Solution | Step 2
\[63=3\times21=3^2\times7,\qquad 504=2^3\times3^2\times7.\]
All remaining factors are prime; group repeated factors as powers.

Final answer

$504=2^3\times3^2\times7$

4. Jan 2022 P2HR · Q10

Medium3 marks

Jan 2022 P2HR Question 10 (3 marks): Number Toolkit – 10 The table gives information about the population and the total amount of money, in dollars, spent on healthcare for two countries in 2016 Country Total population Total spent on healthcare ($) Austria 8.7 × 106 4.2 ×

Show worked solution

Austria spending per person
Austria spending per person:
\[ \frac{4.2\times 10^{10}}{8.7\times 10^6} =4827.586\ldots \]
Luxembourg spending per person
Luxembourg spending per person:
\[ \frac{3.7\times 10^9}{6.3\times 10^5} =5873.015\ldots \]
Difference
Difference:
\[ 5873.015\ldots-4827.586\ldots=1045.429\ldots \]
Convert standard form
To the nearest whole number, this is
\[ 1045 \]

Final answer

$1045$ dollars

5. Elite Practice · Q36

Medium3 marks

Elite Practice Question 36 (3 marks): Number Toolkit – 36 Here is a list of numbers: 2, 9, 15, 17, 21, 25, 27. Write down (a) the two prime numbers (b) a square number that is odd and greater than 10 (c) a cube number. (Total for Question 36 is 3 marks)

Show worked solution

(a) Exactly two factors
$2$ and $17$ are prime ($15=3\times5$, $21=3\times7$).
(b) Square numbers in the list
$9=3^2$ and $25=5^2$; the odd one greater than $10$ is $25$.
(c) Cube numbers
$27=3^3$

Final answer

(a) $2, 17$ (b) $25$ (c) $27$

Number Toolkit: past paper questions & worked solutions

Questions, easiest first

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